If, during your declare attackers step, Barricade Breaker is tapped or is affected by a spell or ability that says it can’t attack, then it doesn’t attack. If there’s a cost associated with having it attack, you aren’t forced to pay that cost, so it doesn’t have to attack in that case either.

2/9/2017

Improvise doesn’t change a spell’s mana cost or converted mana cost.

2/9/2017

When calculating a spell’s total cost, include any alternative costs, additional costs, or anything else that increases or reduces the cost to cast the spell. Improvise applies after the total cost is calculated.

2/9/2017

Because improvise isn’t an alternative cost, it can be used in conjunction with alternative costs.

Improvise can’t be used to pay for anything other than the cost of casting the spell. For example, it can’t be used during the resolution of an ability that says “Counter target spell unless its controller pays .”

2/9/2017

If an artifact you control has a mana ability with in the cost, activating that ability while casting a spell with improvise will result in the artifact being tapped when you pay the spell’s costs. You won’t be able to tap it again for improvise. Similarly, if you sacrifice an artifact to activate a mana ability while casting a spell with improvise, that artifact won’t be on the battlefield when you pay the spell’s costs, so you won’t be able to tap it for improvise.